This question is about writing a paper in mathematics.
I am studying a (partial differential) equation and an algorithm to solve it approximately (finite element method). I need to report in my work a theorem on the approximation error of this algorithm. Such theorem already exists in the paper X: it is proved in a context that is more general than mine for some reasons (moving vs non-moving domain), and slightly less general than mine for other reasons (homogeneous vs non-homogeneous boundary conditions).
Should I report the adapted version of the proof from paper X, after of course appropriately citing it?
The modifications I had to do to the existing proof are mostly "trivial": my estimations are just longer and slightly more technically involved versions of those in X. In one point, however, I make a non-trivial (not so ingenious either) conceptual passage. I need a lot of context to report and prove this conceptual passage, so that rewriting the whole proof in my paper is not so much additional work, and it would be of course clearer.
Long story short, reporting the whole proof seems pedantic and may not be well received from the reviewers, whereas saying "The proof is as in [X]." feels lazy or not informative enough to me. But there may be more leftover space for reporting original content directly related to my publication!